Information on Result #548637
There is no linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-code), because construction Y1 would yield
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- “BPM†bound on codes from Brouwer’s database [i]
- linear OA(724, 36, F7, 21) (dual of [36, 12, 22]-code), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- residual code [i] would yield OA(73, 9, S7, 3), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(713, 37, F7, 11) (dual of [37, 24, 12]-code) | [i] | Truncation | |
| 2 | No linear OOA(713, 36, F7, 2, 11) (dual of [(36, 2), 59, 12]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(712, 36, F7, 2, 10) (dual of [(36, 2), 60, 11]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(712, 36, F7, 3, 10) (dual of [(36, 3), 96, 11]-NRT-code) | [i] | ||
| 5 | No digital (2, 12, 36)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(728, 40, F7, 24) (dual of [40, 12, 25]-code) | [i] | Construction Y1 (Bound) | |